A conventional lubricant supplying system for a transmission of a vehicle, such as shown in Japanese Patent No. 4179364 corresponding to U.S. Patent Application Publication No. 2008/051251 for example, is configured to use surplus of working fluid as a lubricant source, and to supply the oil from the lubricant source to a lubrication system such as gears, after having been cooled down via an air-cooled type cooler. That is, the cooler and the lubrication system are arranged in series with the lubricant source. Also, a safety valve is provided on an upstream side of the cooler in an oil path. A pressure value to open this safety valve is set to a value such that the safety valve will not be opened in an operating state of a lock up clutch which is a supply destination of working fluid, and such that the safety valve will be opened in an off state of the lock up clutch so that supply of oil to the cooler would not be exceed.
In the conventional lubricant supplying system such as described above, there is an inconvenience that, when the oil was stopped up within the cooler, or when a pressure drop in the cooler is increased in case of a low oil temperature, the safety valve is opened, so that lubricant is not sufficiently supplied to the lubrication system such as gears. Further, because the surplus of working fluid is used as the lubricant source, it is needed to increase the size of the oil pump so that the surplus of working fluid can be occurred constantly during low-speed rotation or the like, in order to ensure a volume of lubrication.